Aircraft: CITATION EXCEL (C560XL)
Phase of flight: Climb
Anomaly: Aircraft Equipment Problem Critical; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence

I was pilot monitoring and while climbing out at FL200 we received an amber 'pitch trim' Annunciator. We followed the checklist and determined that something was wrong with a primary or secondary flight control system. The aircraft indicated full nose down trim but the plane was still climbing. The PIC requested my help with the flight controls; as they were very heavy. I notified ATC that we have an emergency and that I was unable to hold assigned altitude. I actually requested a climb as well to get us out of icing as well and get us into VMC. As this was happening; I also manually activated the tail deicing boots just to make sure that icing wasn't the problem. We requested vectors to nearest airport. Unfortunately the weather (wx) there was marginal VFR so we decided to go to ZZZ as the wx was better and it was about an equal time there. We did not want to do an ILS with flight control problems. I requested CFR be standing by at landing; and we then landed without further incident. I have had three emergencies in this type of aircraft; all three were for flight control malfunctions. I believe that there is a systemic problem with this type aircraft that needs to be addressed. Climbing thru FL190 for FL200; we had a pitch trim annunciator. Upon disconnecting the autopilot; the aircraft pitched up aggressively. The pitch trim was full forward and would not move. I tried electric and manual trim. It was frozen. The elevator was shaking significantly. We both had to push full forward on the yoke to arrest the climb. It felt as if the elevator was also frozen. We [advised ATC] and reduced throttles as much as possible to descend. Upon reaching 8500 feet; the trim unfroze and we regained full control. We completed all appropriate checklists and landed uneventfully.What concerns me most is the fact that there was no more trim down available and the aircraft was trying to climb aggressively. The force required to stop the climb was [too much] for just one person. I believe the elevator itself was jammed and the autopilot was trying to compensate for the pitch up by moving the trim towards nose down. When it ran out of trim; we got the annunciator. The fact that the trim froze at that point is somewhat insignificant as trimming up would only aggravate the situation. The trim wheel wouldn't move in either direction until a warmer altitude thawed the cables. Cessna needs to evaluate all XL/XLS aircraft for issues with elevator and pitch trim reoccurring systemic problems. The temporary fixes they have come up with over the last 3 years just seem to mask a deeper issue. CE560XL Flight Crew describes an apparent jammed elevator during climb passing FL200 with the Captain flying. A 'pitch trim' light is annunciated initially and the crew discovers the pitch trim is full nose down with the aircraft needing more to maintain a stable climb. The First Officer's aid is requested by the Captain to help control the aircraft pitch. The flight diverts to a suitable airport.